Omer Karin, Yael Korem, Boaz Dudovich, Uri Alon
Weizmann Institute of Science, Rehovot, Israel 76100
A weekly cycle of 2 work days and 5 lockdown days can provide a good tradeoff between minimising health impact and maximising economic activity. It can keep the infection load low while allowing a sustainable, albeit reduced, economy. It can eradicate the virus without reaching herd immunity, thus preventing a large number of deaths.
[A scientific pre-print is now available at
Current approaches to suppress COVID-19 use testing, contact tracing, social distancing, school closures and full lockdown. The hope is to flatten the infection curve and prevent overload of the medical system until a vaccine becomes available. An Imperial college study  suggested that periodic lockdown for periods of a few weeks, spaced by a week or so, can keep infection below a critical number. The lockdowns are triggered by reaching a threshold number of cases [1,6]. These measures have a large economic cost, and many sectors will show widespread unemployment.
Here we carefully suggest an exit strategy for countries that have enacted a continuous lockdown, and are at the point where this lockdown has succeeded in reducing the number of infections. A weekly cycle of 2 work days and 5 lockdown days or similar strategy, such as a cycle of 4 work days and 10 lockdown days, can keep the infection load low while allowing a sustainable, albeit reduced, economy. It can eradicate the virus without reaching herd immunity, thus preventing a large number of deaths.
The basic idea is to reduce the infectivity, R, defined as the average number of people infected by each infected individual, below 1. When R is below 1, the number of infected people declines exponentially, a basic principle of epidemiology. Infectivity in COVID-19 is estimated at R=2 or more, leading to the observed exponentially growing infection rates. A 2-day work & 5-day lockdown schedule reduces the time a person infects others outside the household. Even better, a cyclic strategy can utilize the fact that most infected people are infectious for only about 3 days, starting about 4 days after being exposed. This seems to apply also to the asymptomatic cases, where people don’t know they have been infected. A 4-day work/10 day lockdown cycle means that those infected during the work days play out their 3-day infectious period during the 10 lockdown days. They return to work without causing new infections. These effects reduce R below one for a wide range of models and parameters.
By “work” we mean release from lockdown with strict hygiene on the same two (or four) weekdays for everyone. This release from lockdown is for the entire population, except for quarantined infected individuals and people in risk groups who may be in quarantine.
Strict hygiene measures will be required to keep R from rising during the work days as people may compensate for the lockdown period by having more social connections and hence more infectivity. During days of lockdown, public spaces can be disinfected to reduce infection through surfaces. Extensive testing and contact tracing can and should be used in parallel, to further reduce average R .
The apparent cost of this strategy is a longer timescale to fully eradicate the virus compared to uninterrupted lockdown. However, one maintains 40% of economic activity. Moreover, after a continuous lockdown is lifted, there is a risk of returning infection. The 2-day workweek can be sustained for far longer than continuous lockdowns, allowing time for a vaccine, effective testing or other measures.
During the “work” days of no lockdown, some people will work, students go to school, children to daycare. Some people will use the work days for services keeping many sectors of the economy working part time.
The cyclic schedule may prevent many people from being fired or put on leave without pay, instead offering them a 40% position (2 out of 5 normal work days). This has economic and psychological benefits.
Cyclic closure is a predictable schedule, with fixed days of the week. This reduces uncertainty. Uncertainty is a problem with polices that rely on triggering lockdown when a certain number of cases are reached . A fixed schedule enhances planning to make work more effective. Other schedules with a 2:5 ratio, such as work shifts, can also be effective.
Regions that adopt this strategy (preferably with other means to keep R<1 such as extensive testing, case isolation and contact tracing ) are predicted to resist infections from the outside. They prevent spread of infections entering from the outside because they give them an average R<1. After enough time, there is a possibility for the virus to be eradicated, in the absence of unknown reservoirs or mutations.
The cyclic strategy can work in regions with insufficient tests, as long as the cyclic schedule can be maintained. This may apply to a large part of the earth’s population.
The exact nature of the intervention can be tuned to optimize economy and minimize infection. The general message is that we can tune containment strategies to balance the health pandemic and the economic crisis.
An intuitive analysis explains how this works. We want the average R to be less than one. The main effect for a 4-day work/10-day lockdown schedule relies on the disease timeline. Exposed individuals are non-infectious for about 3–4 days on average, and are then infectious for another 3–4 days on average . Thus, in a 4/10 strategy, most people who get exposed on workdays will be infectious during lockdown, limiting the spread of the disease. Those that develop symptoms might be infectious for longer, but these individuals will not return to work.
A second effect is reduction of exposure time. Given a fraction f of the time for work, the average R is R=f R_F+(1-f) R_L where R_F is infectivity during work, and R_L is is infectivity during lockdown. Thus, it is sufficient to have f<(1-R_L)/(R_F-R_L). For typical COVID-19 numbers, R_F=2.4 and R_L=0.3, one needs f < 0.3. This is provided by a work frequency of 2 days/week or 4 days/ 2 weeks namely f=2/7=0.28. An important assumption is that risk of infection grows approximately linearly with exposure time in work days.
Using this strategy after an initial lockdown is lifted is not very risky. If the estimated parameters are off or change over time, so that this strategy fails, one will observe a gradual rise in cases, and one can return to lockdown or other strategies .
We tested these strategies using epidemiological models. These range from the classic SIR model (see Figures 1–3) and SEIR model (Figure 4) to models with social contacts (particle simulations of individuals meeting on social networks with short range, long range and random contacts, including the assumption that people meet the same individuals during the work periods). The results are similar in all cases. 1-day or 2- day work weeks are predicted to be sufficient for a range of R that cover the range of estimates for COVID-19 (Figure 3). The policy is resistant to non-compliance to lockdown in which a fraction of the population infects as much as without lockdown.
Technical note on the assumption of linearity of transmission risk with exposure time.